The Partial Second Boundary Value Problem of an Anisotropic Parabolic Equation. (2nd May 2019) - Zhan, Huashui
Abstract : Consider an anisotropic parabolic equation with the variable exponentsv t = ∑ i = 1 n ( b i ( x, t ) v x i p i ( x ) - 2 v x i ) x i + f ( v, x, t ), whereb i ( x, t ) ∈ C 1 ( Q T ¯ ), p i ( x ) ∈ C 1 ( Ω ¯ ), p i ( x ) > 1, b i ( x, t ) ≥ 0, f ( v, x, t ) ≥ 0 . If{ b i ( x, t ) } is degenerate onΓ 2 ⊂ ∂ Ω, then the second boundary value condition is imposed on the remaining part∂ Ω ∖ Γ 2 . The uniqueness of weak solution can be proved without the boundary value condition onΓ 2 .